Techniques for producing low Total Harmonic Distortion in PWM inverters (single-phase or three-phase) have been known to exist in several prior works. In the early days, the carrier-modulated PWM techniques such as the triangular wave comparison type PWM were very popular. For example such techniques are disclosed in: A. Schonung and Stemmler, xe2x80x9cStatic frequency changes with subharmonic control in conjunction with reversible variable speed drive,xe2x80x9d BBC RevI., pp. 555-557, August/September 1964; P. D. Ziogas, xe2x80x9cOptimum voltage and harmonic control of PWM techniques for three phase static UPS systems,xe2x80x9d IEEE Trans. Ind. Appl., vol. IA-16, no. 4, pp. 542-446, July/August 1980; and B. K. Bose and H. A. Sutherland, xe2x80x9cA high performance pulse-width modulator for an inverter-fed drive system using a microcomputer,xe2x80x9d in Conf. Rec. 1982 Ann. Meet. Ind. Appl. Soc., pp. 847-853.
Microcomputer based techniques using preprogrammed PWM patterns have also been utilized. For example in: H. S. Patel and R. G. Hoft, xe2x80x9cGeneralized technique of harmonic elimination and voltage control in thyristor inverter, Part I,xe2x80x9d IEEE Trans. Ind. Appl. vol. IA-9, no. 3, pp. 310-316, March/April 1973; and xe2x80x9cPart II, xe2x80x9cIEEE Trans. Ind. Appl., vol. LA-10, no. 5, pp. 666-673, September/October 1973; F. G. Turnbull, xe2x80x9cSelected harmonic reduction in static dc-ac inverters, xe2x80x9cIEEE Trans. Commun. Elec., vol. 83, pp. 374-478, July 1964; I. J. Pitel, S. N. Talukdar, and P. Wood, xe2x80x9cCharacterization of programmed-waveform pulse-width modulation,xe2x80x9d IEEE Trans. Ind. Appl., vol. IA-16, no. 5, pp. 707-715, September/October 1980; and G. S. Buja, xe2x80x9cOptimum output waveforms in PWM inverters, xe2x80x9cIEEE Trans. Ind. Appl., vol. IA-16, no. 6, pp. 830-836, November/December 1980.
In these techniques, the switching edges of the PWM pattern are computed to satisfy certain performance requirements; the most common of which is controlling the fundamental component and eliminating specified harmonics. Two main disadvantages of these techniques are: slow voltage regulation response due to average voltage control, and phase displacement between the reference sine wave and the filter output varies with the load.
More recent techniques include the time optimal response switching PWM, disclosed in, for example: A. Kernik, D.L. Stechshulte, and D.W. Shireman, xe2x80x9cStatic Inverter with synchronous output waveform synthesized by time-optimal response feedbackxe2x80x9d IEEE Trans. IECI, vol. IECI-24, no. 4, pp. 297-305, 1977; A. Kawamura and R. G. Hoft, xe2x80x9cInstantaneous feedback controlled PWM inverter with adaptive hysteresis,xe2x80x9d IEEE Trans. Ind. Appl., vol. IA-20, no. 4, pp. 769-775, July/August 1984; and P. Ziogas, xe2x80x9cDelta modulation technique in static PWM inverters,xe2x80x9d IEEE Trans. Ind. Appl., vol. IA-17, pp. 289-295, 1981. Other recent techniques include the real-time deadbeat-controlled PWM, disclosed in, for example: K. P. Gokhale, A. Kawamura, and R. G. Hoft, xe2x80x9cDead beat microprocessor control of PWM interter for sinusoidal output waveform synthesis,xe2x80x9d in Conf. Rec. IEEE Power Elect. Spec. Conf., 1985, pp. 28-36 and A. Kawamura, T. Haneyoshi, and R. G. Hoft, xe2x80x9cDeadbeat controlled PWM inverter with parameter estimation using only voltage sensor,xe2x80x9d in Conf Rec. IEEE Power Elec. Spec. Conf, 1986. These techniques have very fast response for load disturbances, but it is also known that these systems have a high THD for non-linear load (crest-load).
The voltage control technique proposed in the present invention uses the perfect control of robust servomechanism problem (Perfect RSP) theory developed in Davison, E. J. and Scherzinger, B., xe2x80x9cPerfect Control of the robust servomechanism problemxe2x80x9d, IEEE Trans. On Automatic Control, 32 (8), 689-702, 1987 (xe2x80x9cDavison et alxe2x80x9d) to ensure perfect tracking of the output voltages under unknown load by providing means for eliminating errors at specified harmonic and at the same time ensuring good transient response. The theory is based on the internal model principle, proposed by Francis, B. A., and Wonham, W. M., xe2x80x9cThe internal mode principle for linear multivariable regulatorsxe2x80x9d, Appl. Math. Opt., vol. 2, pp. 170-194, which states that asymptotic tracking of controlled variables toward the corresponding references in the presence of disturbances (zero steady state tracking error) can be achieved if the models that generate these references and disturbances are included in the stable closed loop systems. In other words, if we include the frequency modes of the references and the disturbances to be eliminated in the control loop, then the steady state error will not contain these frequency modes.
Applying the internal model principle into the output voltages control in a three-phase PWM inverter means that the fundamental frequency mode (50 Hz or 60 Hz) has to be included in the controller since the references vary at this frequency. Elimination of the voltages errors due to the load currents at other harmonics frequency can then be achieved by including the frequency modes of these harmonics into the controller. The perfect RSP theory combines this internal model principle with the optimal state feedback to guarantee stability of the closed loop system and providing arbitrary good transient response.
Similar techniques that use the internal model principle to achieve very low THD output voltage in single-phase PWM inverters have been reported recently in T. Haneyoshi, A. Kawamura, and R. G. Hoft, xe2x80x9cWaveform compensation of PWM inverter with cyclic fluctuating loads, IEEE Trans. Ind. Appl., vol. 24, pp. 582-589, 1988 (xe2x80x9cHaneyoshi et alxe2x80x9d) and Y. Tzou, S. Jung, and H. Yeh, xe2x80x9cAdaptive Repetitive Control of PWM Inverters for Very Low THD AC-Voltage Regulation with Unknown Loads (xe2x80x9cTzou et alxe2x80x9d). In these papers, the control development follows the repetitive control theory developed in T. Inoue, M. Nakano, and S. Iwai, xe2x80x9cHigh accuracy control of servomechanism for repeated contouring,xe2x80x9d in Proc 10th Annu. Symp. Incremental Motion Contr. Syst. Devices, 1981, pp. 258-292; T. Inoue and M. Nakano, xe2x80x9cHigh accuracy control of a proton synchroton magnet power supply,xe2x80x9d in IFAC, vol. 20, 1981, pp. 216-221; and S. Hara, Y. Yamammoto, T. Omata, and M. Nakano, xe2x80x9cRepetitive control system: A new type servo system for periodic exogenous signals,xe2x80x9d IEEE Trans. Automatic Contr., vol. 33, no. 7, pp. 659-666, 1988. Unlike the technique based on the perfect RSP that provides zero steady state error for references or disturbances only at finite specified frequencies, the repetitive control guarantees zero steady state error at all the harmonic frequencies less than half of the sampling period. However, the repetitive control is not easy to stabilize for all unknown load disturbances and cannot obtain very fast response for fluctuating load. In Haneyoshi et al, the latter problem is solved by including a xe2x80x9cone sampling ahead preview controllerxe2x80x9d, and Tzou et al enhances the stability result of Haneyoshi et al by providing an adaptive mechanism for unknown load disturbances.
The inventor would like to point out here that, although the perfect RSP used in this disclosure only eliminates voltage harmonic at a finite specified frequencies, the perfect RSP control is still a very suitable control for a three-phase PWM inverters. It is to be emphasized that in a three-phase system, most of the voltage harmonics, like the triplen harmonics (3rd, 6th, 9th, etc.), are either non-existent, uncontrollable, and/or negligible in values. Therefore, not too many harmonics are left for the control to handle. Moreover, the closed loop stability under unknown load is easier to achieve with the perfect RSP than the repetitive control, and the perfect RSP by itself already provides a good transient response.
The inventor has also successfully combined the perfect RSP control of the voltages harmonics with a fast current controller using a discrete time sliding mode controller, as disclosed in Utkin, V., Guldner, J., Shi, J., Sliding Mode Control in Electromechanical Systems, Taylor and Franci, Philadelphia, Pa., 1999, (xe2x80x9cUtkin et alxe2x80x9d) for limiting the inverter currents under overload condition. This is one of the important features necessary for a UPS, which is not addressed in the repetitive control work of Haneyoshi et al and Tzou et al. The discrete sliding mode controller has been chosen because of the fast and no-overshoot response that it provides. The current controller acts as an inner loop to the perfect RSP control of the output voltages in the outer loop. In this case, the perfect RSP voltage control has been designed by accounting for the extra dynamic introduced by the discrete time sliding mode controller. This way, the stability and robustness of the overall control system are still guaranteed.